Java Game how to make image follow line?

Hello I have a game where circles rotate around the centre of the frame. When I click on two circles a line is drawn between the two circles. The circles are always moving and so is the line. I have an image at the start of the line and I want it to move along the line at stop at the end of the line. I knowhow to start the image at the start but I don't know how to move the image along the line. How can I move the image along the line?

Here is my code:

   public class ship {

public int sx,sy,ex,ey;
public boolean arrived,sel1,sel2;
public int amountOfPop = 0;

public int fc = -1,sc = -1;


public ship(int sx,int sy,int ex,int ey,int aop){
    this.sx = sx;
    this.sy =sy;
    this.ex = ex;
    this.ey =ey;
    this.amountOfPop = aop;



}


public void tick(){


}

public void render(Graphics g){
    g.setColor(Color.blue);
    g.drawLine(sx, sy, ex, ey);
}

 }

sx and sy are the starting x and starting y. ex and ey is where the image should finish. Please help me.

Answer

I'm going to explain this using Vector mathematics. I would also recommend to store your x and y values as such, as it makes it easier to maintain. Here's an example:

public class Vector2 {

    public float x;
    public float y;


    public Vector2(float x, float y) {
        this.x = x;
        this.y = y;
    }

    public static float length(float x, float y) {
        return Math.sqrt(x * x + y * y);
    }

    public static float distance(Vector2 first, Vector2 second) {

        return length(second.x - first.x, second.y - first.y);
    }

    public static Vector2 direction(float x, float y) {
        return new Vector2(x / length(x, y), y / length(x, y));
    }
}

You'll want to give your ship a Vector2 to indicate its current position, the start position, the target position, and one for the direction. You'll also need a speed variable which indicates the rate at which your image will move (you could just use 1f if you like), and a distance variable to indicate the distance from the current position:

private Vector2 position;

private Vector2 start;
private Vector2 target;
private Vector2 direction;

private float speed;

private float distance;

...


public Ship(Vector2 position, Vector2 target, float speed, ...) {
    this.position = position;

    // Initialize start as a new Vector2 with the same x and y coordinates as position
    this.start = new Vector2(position.x, position.y);
    this.target = target;

    distance = Vector2.distance(start, end);
    direction = Vector2.direction(end.x - start.x, end.y - start.y);


    ...
}

public void tick() {
    position.x += direction.x * speed;
    position.y += direction.y * speed;

    if (Vector2.distance(start, position) >= distance) {
        // The ship has reached the target
    }


    ...
}

I'm assuming your tick() method is where you're performing your logic. What we're doing here is adding the distance * speed to the current position of the ship, making it travel along the imaginary line between the start position and the target.

If your start and target points are changing as you say, all you need to do is update the distance and direction variables in your tick() method:

public void tick() {
    distance = Vector2.distance(start, end);
    direction = Vector2.direction(end.x - start.x, end.y - start.y);


    ...
}

---

Equations:

Length:

Distance:

Direction:

---

The Vector2 class in this example is very basic and can definitely be improved upon. I suggest learning more about Vector mathematics, as well as taking a look at existing implementations of Vector mathematics and calculations to get a better idea on the subject. Here's one such implementation of a Vector2 class in libGDX.